On finite commutative loops which are centrally nilpotent
Let be a finite commutative loop and let the inner mapping group , where is an odd prime number and . We show that is centrally nilpotent of class two.
Let be a finite commutative loop and let the inner mapping group , where is an odd prime number and . We show that is centrally nilpotent of class two.
Let be a loop such that is square-free and the inner mapping group is nilpotent. We show that is centrally nilpotent of class at most two.
Let be a finite group with a dicyclic subgroup . We show that if there exist -connected transversals in , then is a solvable group. We apply this result to loop theory and show that if the inner mapping group of a finite loop is dicyclic, then is a solvable loop. We also discuss a more general solvability criterion in the case where is a certain type of a direct product.
Page 1